Question

4. Suppose that we have a set of temperature measurements in degree Celsius whose variance is

25(◦C)2. What is the standard deviation of same set of measurements in degree Fahrenheit?

(The formula connecting degree Celsius and degree Fahrenheit is: Y (◦F) = 1.8X(◦C) + 32.)

please explain clearly

Answer 1

We are using an important result

If y=a+bx,then s.d(y)= b s.d(x), i.e standard deviaton is independent of the choice of origin but depends on the choice of the scale

Proof:- Suppose that for given value of x, i.e xi for all i=1(1)n,there are values of yi,such that yi=a+bxi  for all i=1(1)n

(here a is origin parameter and b is scale parameter)

from knowledge of descriptive statistics,we know the mean is

So,

Also from knowledge of descriptive statistics,we know the standard deviation is

So

=

Hence proved

So from the above result

Variance is 25 (C)^2

So standard deviation is 5(C)

using the equation Y=1.8X(C)+32

and from the above result sd(y)= 1.8sd(x)

So sd (y)=1.8*5=9( in fahrenheit)(ANSWER)

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